Basics of Fluid Mechanics, 2014a

430 CHAPTER 11. COMPRESSIBLE FLOW ONE DIMENSIONAL
Table -11.4.
The Isothermal Flow basic parameters (continue)
M
4fL
D
P
P ∗ P 0
P 0
∗
ρ
ρ ∗ T 0
T 0
∗
0.75000 0.03095 1.1269 1.0255 1.1269 0.97344
0.80000 0.00626 1.056 1.009 1.056 0.98700
0.81000 0.00371 1.043 1.007 1.043 0.98982
0.81879 0.00205 1.032 1.005 1.032 0.99232
0.82758 0.000896 1.021 1.003 1.021 0.99485
0.83637 0.000220 1.011 1.001 1.011 0.99741
0.84515 0.0 1.000 1.000 1.000 1.000
11.6.6 Isothermal Flow Examples
There can be several kinds of questions aside from the proof questions 18 . Generally,
the “engineering” or practical questions can be divided into driving force (pressure
difference), resistance (diameter, friction factor, friction coefficient, etc.), and mass
flow rate questions. In this model no questions about shock (should) exist 19 .
The driving force questions deal with what should be the pressure difference to
obtain a certain flow rate. Here is an example.
Example 11.15:
A tube of 0.25 [m] diameter and 5000 [m] in length is attached to a pump. What
should be the pump pressure so that a flow rate of 2 [kg/sec] will be achieved? Assume
that friction factor f =0.005 and the exit pressure is 1[bar]. [ The ] specific heat for the
gas, k =1.31, surroundings temperature 27 ◦ J
C, R = 290
Kkg
. Hint: calculate the
maximum flow rate and then check if this request is reasonable.
Solution
If the flow was incompressible then for known density, ρ, the velocity can be calculated
by utilizing ΔP = 4 f̷L U 2
D 2g . In incompressible flow, the density is a function of the
entrance Mach number. The exit Mach number is not necessarily 1/ √ k i.e. the flow is
not choked. First, check whether flow is choked (or even possible).
18 The proof questions are questions that ask for proof or for finding a mathematical identity (normally
good for mathematicians and study of perturbation methods). These questions or examples will appear
in the later versions.
19 Those who are mathematically inclined can include these kinds of questions but there are no real
world applications to isothermal model with shock.